On the bootstrap in cube root asymptotics

Canadian Journal of Statistics

Volumn 34, Issue 1, 2006, Pages 29-44

  Léger, Christian ^a   Macgibbon, Brenda ^b  

^a UNIVERSITÉ DE MONTRÉAL   (Canada)

^b UNIVERSITÉ DU QUÉBEC À MONTRÉAL   (Canada)

Author keywords

Bootstrap; Confidence interval for the mode; Counterexample; Cube root asymptotics; Least median of squares; Resampling

Indexed keywords

EID: 33744761802     PISSN: 03195724     EISSN: None     Source Type: Journal    
DOI: 10.1002/cjs.5550340104     Document Type: Article

References (21)

1. N. Altman & C. Léger (1997). On the optimality of prediction-based selection criteria and the convergence rates of estimators. Journal of the Royal Statistical Society Series B, 59, 205-216.
2. D. F. Andrews, P. J. Bickel, F. R. Hampel, P. J. Huber, W. H. Rogers & J. W. Tukey (1972). Robust Estimates of Location. Princeton University Press.
3. S. Arunkumar (1972). Nonparametric age replacement policy. Sankhyā, Series A, 34, 251-256.
4. R. Beran (1984). Bootstrap methods in statistics. Jahresbericht der Deutschen Mathematiker-Vereinigung, 86, 14-30.
5. H. Chernoff (1964). Estimation of the mode. Annals of the Institute of Statistical Mathematics, 16, 31-41.
6. A. C. Davison & D. V. Hinkley (1997). Bootstrap Methods and their Application. Cambridge University Press.
7. B. Efron & R. J. Tibshirani (1993). An Introduction to the Bootstrap. Chapman & Hall, London.
8. P. Groeneboom (1989). Brownian motion with a parabolic drift and Airy functions. Probability Theory and Related Fields, 81, 79-109.
9. P. Hall (1988). Theoretical comparison of bootstrap confidence intervals. The Annals of Statistics, 16, 927-953.
10. P. Hall (1992). The Bootstrap and Edgeworth Expansion. Springer, New York.
11. J. Kim & D. Pollard (1990). Cube root asymptotics. The Annals of Statistics, 18, 191-219.
12. K. Knight (1989). On the bootstrap of the sample mean in the infinite variance case. The Annals of Statistics, 17, 1168-1175.
13. C. Léger & R. Cléroux (1992). Nonparametric age replacement: Bootstrap confidence intervals for the optimal cost. Operations Research, 40, 1062-1073.
14. C. Léger & B. MacGibbon (2005). On the bootstrap in cube root asymptotics. Technical Report CRM-3186, Centre de recherches mathématiques, Université de Montréal, Montréal (Québec).
15. C. Léger & J. P. Romano (1990). Bootstrap choice of tuning parameters. Annals of the Institute of Statistical Mathematics, 4, 709-735.
16. J. E. Marsden & A. J. Tromba (1976). Vector Calculus. W. H. Freeman, San Francisco.
17. D. N. Politis, J. P. Romano & M. Wolf (2001). Subsampling. Springer, New York.
18. D. Pollard (1989). Asymptotics via empirical processes. Statistical Science, 4, 341-354.
19. P. J. Rousseeuw (1984). Least median of squares regression. Journal of the American Statistical Association, 79, 871-880.
20. J. Shao & D. Tu (1995). The Jackknife and Bootstrap. Springer, New York.
21. M. Zarepour & K. Knight (1999). Bootstrapping point processes with some applications. Stochastic Processes and their Applications, 84, 81-90.